A variety of mops and other cleaning implements have been developed for cleaning and dusting floors and other surfaces. Many mops in common usage, such as string mops, have a cleaning surface that is repeatedly reused. In certain settings, such as hospitals and nursing homes, where there are concerns over hygiene and safety in dealing with hazardous chemical or biological wastes that may be spilled or otherwise present on floors, it is desirable to use a floor mop with a cleaning portion that is not reused, but instead is replaced between cleanings. With such mops, a disposable cleaning media, typically a flexible sheet of cleaning material, is secured to the mop head and removed after the cleaning operation is completed. The mop head is then reloaded with a fresh cleaning sheet prior to its next use.